a. A closed cylindrical can is to hold 1000cm^3 of liquid. How should we choose the height and radius of this can to minimize the amount of material need to manufacture the can?

Question

b.a manufacturer wants to design a open box having a square base and surface of 108cm^2. What dimensions will produce a box with minimum volume?

Steve · Accepted Answer

πr^2 h = 1000, so h = 1000/(πr^2)
surface area is

a = 2πr^2 + 2πrh
= 2πr^2 + 2000/r

da/dr = 4πr - 2000/r^2
= 4(πr^3 - 500)/r^2
da/dr=0 when r = ∛(500/π)
thus, h = 100/∛(250π)

Do the other along the same way.

dinesh · Answer

steve bro... hw bout the b? plz tell me...

Rick · Answer

dinesh bro... the b is the same as the a

dejen · Answer

h=234.43

abebe · Answer

answer

abebe · Answer

-1+x^2